The present invention relates generally to a method and apparatus for linearity error compensation in electronic devices, and more particularly to phase-shift exponential processing methods and apparatus for compensating linearity errors (such as harmonic or intermodulation distortion).
Linearity errors, also known as nonlinear distortion, in electronic devices are caused by many different factors, primarily in the analog electronics of a system, such as buffer amplifiers, power amplifiers, sample-and-hold amplifiers, analog-to-digital converters, digital-to-analog converters, or electro-mechanical components such as microphones and loudspeakers. These devices introduce nonlinear effects into the system such as asymmetry in the input/output function, clipping, overloading effects, harmonic distortion, and intermodulation distortion.
For example, although the output y of an ideal amplifier is related to its input x by the linear equation y=gx (where g is the gain of the amplifier), the relationship between the input and output of a real amplifier is characterized by the equation y=a0+a1x+a2x2+a3x3+ . . . , where the exponential terms (e.g., a2x2, a3x3) represent nonlinear distortion introduced by the real amplifier. Other real signal processing devices introduce similar nonlinear distortion into their output. As a result, the outputs of real signal processing devices differ from the desired, ideal outputs.
Linearity errors in electronics severely limit the performance of systems. Linearity errors typically increase as the speed or bandwidth of the device is increased, which limits the resolution or dynamic range of the device. Designers typically face the challenge of trading off resolution of the device with its speed. Increasing the speed and resolution of electronics can offer numerous advantages, including the following: improved dynamic range which increases call capacity in cellular communications systems; increased modulation density (such as larger Quadrature Amplitude Modulation grid spacing) for wider bandwidth digital communications; wideband analog-to-digital conversion or digital-to-analog conversion for compact, universal software-reconfigurable transceivers; improved accuracy of Radar systems and medical imaging equipment; improved speech recognition by compensating for linearity errors in microphones; and high-performance test equipment such as oscilloscopes, spectrum analyzers, or data acquisition systems.
Many electronic systems such as receivers and test equipment use filtering to compensate for gain and phase errors across frequency. A pseudo-random noise signal is periodically injected into the system and the output is re-calibrated for constant gain and phase performance. Since this prior art technique uses a linear filtering operation, it does not correct nonlinear distortion and therefore does not improve the dynamic range.
A common prior art technique for reducing linearity errors is by adding noise or xe2x80x9cditherxe2x80x9d to the system to essentially randomize the nonlinear distortion. Statistically, dither signals can cause the nonlinear distortion to be signal independent, uniformly distributed white noise. This technique can offer up to 10 dB reduction in harmonic and intermodulation distortion, but at the expense of increasing the noise in the system, which decreases the signal-to-noise ratio.
Another prior art technique for linearity error compensation is a static look-up table (such as a read-only memory) to correct the digital signal. The static look-up table is a two-column table, where the first column contains amplitudes of all possible output signals output by the signal processing device, and where the second column contains the corresponding desired corrected output signal amplitudes. When the signal processing device produces an output signal, the output signal""s amplitude is used as an index into the static compensation table, which outputs the corresponding corrected output value. This technique is effective for errors caused by resistor component variance in the comparator ladder of analog-to-digital converters and can provide up to 10 dB reduction in harmonic distortion. However, most current high-performance converters use laser trimmed resistors, so this type of error is minimal. In addition, researchers have realized that this type of correction improves the dynamic range of the converter only near the calibration frequency. The static compensation table can be as large as the number of digital states (for example, an n-bit analog-to-digital converter has 2n digital states) so a 12-bit analog-to-digital converter requires a compensation table of up to 4096 memory bins.
Referring to FIG. 1, another prior art technique for linearity error compensation is phase-plane compensation 10, which is a dynamic approach since it accounts for errors that are a function of both amplitude and frequency. Like static compensation, a look-up table 40 is used to correct the digitized samples 15, but in this case, the lookup table 40 is indexed by the digital signal 15 and the estimated slope 35 of the signal (to account for frequency), as shown in FIG. 1. This technique accomplishes all that static compensation does but yields improved performance for its ability to compensate errors that are a function of frequency. This technique typically provides 10-15 dB reduction in harmonic distortion. This technique is more hardware-intensive than static compensation since it needs to estimate the slope of the signal 5 and use the slope to index a larger look-up table 40. For this technique, there is essentially one static compensation table for each slope. So if there are M slopes, each slope getting its own static table, then the size of the table 40 is Mxc3x972n.
A typical compensation table for an 8-bit device may occupy 32,768 memory bins (256 amplitudes, 128 slopes). Also, inaccurate slope estimates significantly degrade the performance. In addition, this technique is not suitable for super-Nyquist input frequencies (signals above the Nyquist frequency) due to the ambiguity in the slope. Super-Nyquist compensation is necessary in receiver applications that use intermediate frequency (IF) sampling to alias desired signals down to baseband without the use of mixers (which are typically inaccurate and bulky).
Another prior art technique for linearity error compensation is polynomial compensation, for example, as disclosed in U.S. Pat. No. 5,594,612 to Henrion. This technique uses a polynomial power series to compensate for linearity errors by adjusting the polynomial coefficients to minimize the amplitude of the linearity errors. For example, the output signal, x, of a device is processed with a polynomial power series, y=a0+a1x+a2x2+a3x3+ . . . , to output a compensated signal, y; the polynomial coefficients a0, a1, . . . , are iteratively adjusted and the system output is monitored until the linearity errors are below a certain threshold. However, this technique assumes that the linearity errors generated by the device being compensated are accurately modeled with the polynomial power series. An important parameter missing in this model is the phase-shift of the higher-order linearity error distortion terms (e.g., a2x2, a3x3); the level of attenuation of the linearity errors suffers greatly without accounting for phase-shift since this technique assumes that the device generates linearity errors which are either in-phase or out-of-phase with the desired fundamental signal. Many devices generate linearity errors with arbitrary phase-shift, so accurately accounting for the phase-shift of the linearity errors in the device is necessary for accurate compensation. In addition, the polynomial compensation technique does not accurately compensate linearity errors over a wide range of input frequencies, since the polynomial model cannot accurately model linearity errors that change over frequency. Also, the polynomial compensation technique uses integer exponentials, which may not accurately model the linearity errors of the device.
Embodiments of the present invention are directed to methods and apparatus for providing linearity error compensation that overcome drawbacks of the prior art discussed above. Unlike the prior art gain/phase calibration, the present invention provides gain/phase calibration in addition to linearity error compensation. Unlike the prior art dither method, the present invention provides linearity error compensation without increasing the noise. Unlike the prior art static compensation, the present invention provides linearity error compensation across a wide range of frequencies. Unlike the prior art phase-plane compensation 10, the present invention does not require slope estimates and is capable of super-Nyquist error compensation; the present invention""s kth order phase-shift exponential model uses approximately k amplitude factors and k phase-shift factors to model the system, where k is typically in the range of 3 to 5, which is much less memory than required by phase-plane compensation. Unlike prior art polynomial compensation, the present invention uses phase-shift to accurately cancel the linearity errors, uses frequency-dependent processing to cancel linearity errors over a wide range of frequency, and may use non-integer exponentials to more accurately model and cancel the linearity errors.
In one general aspect, the invention features a compensator for compensating linearity errors in a device generating a fundamental signal and linearity error distortion signals. The compensator includes an exponentiator for generating a compensation signal and a phase-shifting unit for introducing a phase-shift between the fundamental signal and the compensation signal such that the linearity error distortion signals are canceled and the fundamental signal is maintained.
In another general aspect, the exponentiator in the compensator includes a power unit for generating an exponentiated compensation signal. The power unit may be used to generate an integer or non-integer exponentiated signal. Frequency-dependent gain units for adjusting the exponentiated compensation signals amplitude may be connected to the power unit or to the phase-shift unit or both. An adder may be included to combine the exponentiated compensation signals.
In another general aspect, the compensator includes a set of adders connected to a set of the phase-shifting units for adding a set of compensation elements to generate a set of factored compensation signals. The exponentiation is accomplished with a multiplier to combine the set of factored compensation signals. Frequency-dependent gain units for adjusting each factored compensation signal""s amplitude may be connected to each phase-shifting unit or each adder or both.
In yet another general aspect, the compensator includes an adder connected to the phase-shifting unit for adding a compensation element to generate a factored compensation signal. The exponentiation includes a power unit for generating an exponentiated compensation signal and a multiplier for combining the factored compensation signal and the exponentiated compensation signal.
In still another general aspect, the invention features a frequency-dependent phase-shifting unit. In even another general aspect, the phase-shifting unit""s compensation parameters or the exponentiator""s compensation parameters are adjusted according to the amplitude of the fundamental signal.
In another general aspect, the compensator is connected to the device and the compensator precedes the device. The device may include a digital-to-analog converter. Alternatively, in another general aspect, the compensator is connected to the device and the compensator follows the device. The device may include an analog-to-digital converter.
In still another general aspect, the compensator""s phase-shifting unit""s compensation parameters and the exponentiator""s compensation parameters are calibrated according to the measured amplitude and phase of the fundamental signal and linearity error distortion signals.
In even another general aspect, the invention features a compensation system for compensating linearity errors including a device for generating a fundamental signal and linearity error distortion signals, an exponentiator for generating a compensation signal, and a phase-shifting unit for introducing a phase-shift between the fundamental signal and the compensation signal such that the linearity error distortion signals are canceled and the fundamental signal is maintained. The phase-shifting unit""s compensation parameters and the exponentiator""s compensation parameters arc calibrated according to the measured amplitude and phase of the fundamental signal and linearity error distortion signals.
In yet another general aspect, the invention features a model for modeling linearity errors in a device generating a fundamental signal and linearity error distortion signals including an exponentiator for generating a modeling signal and a phase-shifting unit for introducing a phase-shift between the fundamental signal and the modeling signal. The phase-shifting unit""s model parameters and the exponenitiator""s model parameters are calculated according to the measured amplitude and phase of the fundamental signal and linearity error distortion signals.
In another general aspect, the invention features a method for calibrating a compensation system that cancels linearity error distortion signals generated by a device and maintains a fundamental signal generated by the device. The method of calibrating includes steps of injecting test signals into the compensation system, measuring the amplitude and phase of the linearity error distortion signals and the fundamental signal, and calculating a set of compensator coefficients. The step of calculating the set of compensator coefficients includes solving for a set of phase-shifting compensation parameters and a set of exponentiator compensation parameters.
The step of calculating the set of compensator coefficients may include a step ignoring linearity error distortion signals with amplitudes smaller than a pre-determined threshold.
In even another general aspect, the step of calculating the set of compensator coefficients may include a step of repeating the step of calculating the set of compensator coefficients to generate several sets of compensator coefficients for a cascaded compensator. The method may include a step of mathematically combining the several sets of compensator coefficients into a single combined set of compensator coefficients for a non-cascaded compensator having substantially the same performance as the cascaded compensator.
In still another general aspect, the step of calculating a set of compensator coefficients includes a step of setting the phase-shifting compensation parameters to be substantially equivalent to the measured phase of the linearity error distortion signals and setting the amplitudes of the corresponding exponentiator compensation parameters to be the approximate negative of the measured amplitude of the linearity error distortion signal.
In another general aspect, the step of injecting test signals into the compensation system includes a step of injecting one or more sinusoidal test signals, and the step of measuring the amplitude and phase of the linearity error distortion signals and the fundamental signal includes a step of using trigonometric identities to convert powers of sinusoidal functions to sinusoidal functions of harmonics.
In yet another general aspect, the step of calculating a set of compensator coefficients includes iteratively optimizing the set of phase-shifting compensation parameters and the set of exponentiator compensation parameters.
In another general aspect, the invention features a method of compensating linearity errors in a device generating a fundamental signal and linearity error distortion signals. The method includes steps of exponentiating a compensation signal to generate an exponentiated compensation signal and phase-shifting the compensation signal or the exponentiated compensation signal to introduce a phase-shift between the fundamental signal and the exponentiated compensation signal such that the linearity error distortion signals are canceled and the fundamental signal is maintained.
In even another general aspect, the step of exponentiating comprises a step of using a power method to generate the exponentiated compensation signal. Also, the step of using a power method includes using an integer power method to generate an integer exponentiated signal or using a non-integer power method to generate a non-integer-exponentiated signal.
In still another general aspect, the step of exponentiating includes a step of adjusting the amplitude of the exponentiated compensation signal based on the frequency of the fundamental signal.
In yet another general aspect, the step of phase-shifting includes several steps of phase-shifting and the step of exponentiating includes several steps of using a power method to generate a several exponentiated compensation signals. The method may further a step of adding the several of exponentiated compensation signals together.
In another general aspect, the step of phase-shifting includes several steps of phase-shifting to generate several phase-shifted compensation signals. The method further includes a step of adding several compensation elements to the several phase-shifted compensation signals to generate several factored compensation signals. The step of exponentiating includes multiplying the several factored compensation signals.
In yet another general aspect, the step of phase-shifting includes generating a phase-shift based on the frequency of the fundamental signal. Also, the step of phase-shifting may include adjusting the phase-shift compensation parameters according to the amplitude of the fundamental signal or the step of exponentiating may include adjusting the exponentiation compensation parameters according to the amplitude of the fundamental signal.
In even another general aspect, the compensation signal is the output of the device. The device may be for converting signals from analog to digital.
In another general aspect, the invention features a method of compensating linearity errors. The method includes steps for generating a fundamental signal and linearity error distortion signals, exponentiating a compensation signal to generate an exponentiated compensation signal, and phase-shifting the compensation signal or the exponentiated compensation signal to introduce a phase-shift between the fundamental signal and the exponentiated compensation signal such that the linearity error distortion signals are canceled and the fundamental signal is maintained. The phase-shifting compensation parameters and the exponentiation compensation parameters are calibrated according to the measured amplitude and phase of the fundamental signal and linearity error distortion signals.
In another general aspect, the invention features a method of modeling linearity errors in a device generating a fundamental signal and linearity error distortion signals. The method includes steps of exponentiating a modeling signal to generate an exponentiated modeling signal, and phase-shifting the modeling signal or the exponentiated modeling signal to introduce a phase-shift between the fundamental signal and the exponentiated modeling signal. The phase-shift model parameters and the exponentiation model parameters are calculated according to the measured amplitude and phase of the fundamental signal and linearity error distortion signals.